The existence of a second resonance of the Higgs field with a mass
$(M_H)^{\rm theor} = 690 \pm 10 ~({\rm stat}) \pm
20 ~({\rm sys})~ {\rm GeV}$ has been recently proposed.
By analyzing the ATLAS Run2 results on charged 4-lepton final state in
the region of invariant mass 620$\div$740 GeV, we show that they are consistent
with the presence of a new resonance of mass $(M_H)^{\rm
exp}=660\div 680$ GeV which could represent the hypothetical second
resonance. In fact, on the one hand, the observed mass would fit well with the
theoretical range. On the other hand, the ATLAS data
reproduce to high accuracy the expected correlation, between
resonating peak cross section $\sigma_R(pp\to H \to 4l)$ and the
ratio $\gamma_H=\Gamma_H/M_H$, which is mainly determined by the
lower-resonance mass $m_h=$ 125 GeV. Furthermore, indications for a new
resonance in the same mass range are also present in i) the ATLAS search for resonances
decaying into photon pairs and ii) recent
public CMS results. We emphasize that, when comparing with a
definite theoretical prediction, local excesses should {\it not}
be downgraded by the look-elsewhere effect. Therefore, considering the presumably
small correlation among the different results, the cumulated
statistical significance might be close to the traditional 5-sigma
discovery level.